First slide

Gravitaional potential energy

Question

The radius in kilometers to which the present radius of the earth (R=6400 km) is to be compressed so that the escape velocity is increases to ten times is

Easy

A

6.4
B

64
C

640
D

4800

Solution

$\large V \propto \frac{1}{{\sqrt R }} \Rightarrow \frac{{{R_1}}}{{{R_2}}} = {\left( {\frac{{{V_2}}}{{{V_1}}}} \right)^2}$
$\large \frac{{{R_1}}}{{{R_2}}} = 100 \Rightarrow {R_2} = \frac{{{R_1}}}{{100}} = 64km$

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